Related papers: An Injectivity Theorem

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally K\"ahler morphism $\pi \colon X \to \Delta$ from $X$ to a complex…

One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Another implication of the axiom, discussed in the…

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

Given a generalization of Lebesgue decomposition we obtain an extension to the finitely additive setting of the theorems of Halmos and Savage and of Yan.

We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated…

We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.

This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the…

We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…

Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.

The \begin{it} Invariance Theorem \end{it} of M. Gerstenhaber and S. D. Schack states that if $\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category…

We show that the local and global invariant cycle theorems for Hodge modules follow easily from the general theory. We also give some remarks about related papers.

We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.

We study projective manifolds with nonamenable and non-residually finite fundamental groups. We generalize the uniformization theorem of our earlier note. We generalize a classical theorem of Maltsev about finitely generated subgroups of…

Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.

We prove the abundance theorem for semi log canonical surfaces in positive characteristic.

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.

Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap…

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…

The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that…